pros:
-massive damage(atomic nukeSSS)
-nice stun if mastered.. as well as keeps champs inside for a period if they dont want to be stunned.
-fair movespeed.
-if timed right or during clash, DM can make or break the outcome of the battle.
-AP scales continuously w/ or w/o items(if you time right for baleful strike)
-end game AP is awesome.
-gonna get kills and assists.

cons:
-soft, really soft(he can even be considered a glass cannon).
-mana runs out quickly(thanks to clarity, this may be the least of your problems)
-quite slow compared to most champs.
-hard to set up(thanks to flash 'which i consider one of the best if not the best summoner spell' this might not be much of a problem timed and done right)

general draft of item build:
FIRSTLY.. [call mid lane even before the game starts]
..get DORANS RING and a blue pot(if you feel the enemy will be aggro, take a red pot)your main objective is to stay in lane until about level 6 where you can get your first kill. just BS the dying minions(at lvl 1, its hard.. so here is a TIP, when a minion is about 1/4 hp, attack it then quickly drop BS(Q) since the animation will only give .2 seconds delay which is most likely gonna be yours.. another tip, by level 2 or 3, your mana pool will be low, the moment you hit about 1/3 mp, use clarity, then when you hit 3/4 mp while clarity is in CD, use the pot(if its blue). this will most of the time keep you in the lane long enough to scale up your AP.

NEXT..the moment you hit 5 or 6, try harassing your lane opponent but be careful of your mana, you may have clarity ready by this time again so use it in the right moment(1/3 mana is missing).. the moment the enemy's hp goes about below 1/3 and you have all 3 skills(BS EH PB) ready. flash in.. cast BS, EH, then PB, then BS again for the clincher.. its about bye bye for your enemy or if not, go home or DIE.. p.s. be careful with EH(you should know the time when to stun the enemy or place it further to keep him form going any further like near the enemy turret. another TIP, the max cast range of EH is the center of the circle, so it somewhat extends further if you place it right.. and ANOTHER THING.. flash makes EH easier to place, so use it wisely, its your main escape and initiation skill.

continuing, by about level 8 or 9, start calling a lane switch for one that can solo while you start ganking, assisting, hunting, KILLING, DOMINATING. you will still need you team mates to act in here, even if you can kill them, really. because of your stun, its almost about death or run run run for the enemy as you flash and stun, while spamming BS and PB. dont be afraid of the CD of your PB since its better throwing it more than just saving it for nothing. in this STAGE of the GAME, you kind should have bought atleast boots and the ability book, this is well enough but if possible, haunting guise and sorcerer boots. the moment you make this too items, ASAP pls, its about all fun from here.

as the game progresses, just continue ganking and farming AP(minions or champs) then start build HP AP items like rylai, rod of ages.. or go with items like void staff, zhonyas, nashors. nashor may be one of his core items after haunting and sorc boots since it gives AP and CD reduc.

TIPS and NOTES(some may be repeated)
-last hit minions with BS to scale AP off the roof.
-last hit champs with BS for more AP than minions, or with PB for AP and regen mana.
-flash in for better aiming at event horizon getting the stun.. then use DM exactly right after.. this takes practice but is very rewarding if you hit the combo, because after that, use BS then PB, then its bye bye beautiful for any non tank or hp scaled champ
-spam clarity the moment mana hits below 1/2(except at level 1, which would be 1/3)
-gank gank gank, kills or assist will do.
- if there is no enemy veigar in the opposing team, get archangels staff, the gained mana is just too good and since you spam spells like crazy.
- use DM to farm farm farm, during mid to late game, and for defending or pushing. BUT, BUT save it when some champs are near, because you will be using it for clashing.
- try staying behind the team or in the sides, then just flash in and drop DM and EH during clashes.. it can take out 1/2 hp of the carries and mages, so you can finish of with BS and PB.

** this is the solo lane veigar, if laning with another team mate, there is yet another build i may make since it doesnt follow the same early game flow.
** practice practice and practice makes veigar really strong, yet many find him weak than annie, or less of a potential team game champ. which i strongly disagree because those guys only know pub stomping. flash stun gank is one very versatile thing with veigar since his stun is longer than annis, and the damage output and late game potential is way better. i like using annie and she is strong, but veigar is my fave sofar.. ** recently replacing anivia **
** as mentioned, archangels is if there is no veigar in the other team, other than that.. skip it.
** im not that of high level, so no runes, and for masteris, it isnt maxed out, maybe in the future when i hit 30.
** veigar doesnt really need runes or masteries, but if you have, its always an additional.

** peace out **

extension:
good team mates( champs that work well while ganking or clash)

League of Legends is a team based, real time strategy game set in a mythical world of swords & magic where epic battles decide the fate of mystical nations. Game players take on the role of a Summoner who conjures and controls champions to fight for them at the Institute of War. During game play champions gain experience and items to enhance their skills and abilities. How players develop and play their champions can be the difference between a crushing defeat or a glorious victory!